Light entering the eye passes through several refractive elements including the cornea, the aqueous, the lens, and the vitreous before forming an image on the retina. Several vision problems are caused by the formation of defocused images on the retina due to eyeball or corneal deformations. Some common vision problems include myopia, presbyopia, hyperopia, and astigmatism. Refractive corneal surgery has been proven to be effective in compensating for these vision problems by reshaping the cornea, the most accessible refractive element of the eye, in a way so that the image focuses correctly on the retina.
Corneal shape correction can be achieved with an invasive surgical procedure such as radial keratectomy, Kerato-mileusis, and Kerato-phakia. A non-invasive procedure such as Photorefractive Keratectomy ("PRK") can also be used in which the corneal surface is ablated step-by-step with ultra-violet (UV) high-power laser pulses to achieve a desired shape. Another non-invasive procedure is Laser Photo Thermal Keratoplasty ("LPTK") in which the cornea is shaped by thermal effects resulting from irradiation of a laser beam.
The corneal shape determines the corrected vision acuity. The correction in the corneal curvature is conventionally measured in diopters, like many other quasi-spherical optical surfaces. Diopters are defined as a reciprocal of the focal length measured in meters. It is known that a deviation by 1 diopter from the desired correction can result in a visual acuity as low as 20/40. Therefore, accurate measurements of the corneal shape during the surgical procedure in order to minimize the surgical errors becomes critical.
PRK methods irradiate the patient's eye by a pulsed laser emitting at a wavelength in an ultra-violet (UV) spectral region in which the corneal tissue is highly absorptive. The corneal tissue is ablated by the high-energy laser pulses and the ablation depth produced by a laser pulse depends on the energy density or "fluence" of the laser pulse. On average in a typical PRK operation, a tissue depth of approximately 0.2.about.0.4 .mu.m can be ablated per pulse with a laser fluence ranging from about 100 mJ/cm.sup.2 to about 300 mJ/cm.sup.2.
Two types of PRK procedures are commonly used, one using a uniformly expanded laser beam and another one using a focused scanning beam. The PRK technique based on a uniform beam expand the UV laser beam to approximately the size of the entire cornea. Accurate diameter control may be achieved by using an iris (i.e., a diaphragm). This method can be used in a treatment for the myopia, hyperopia or presbyopia, but not for astigmatism. The scanning beam PRK method focuses the laser beam to a small spot diameter on the cornea (e.g., approximately 1 mm). This small spot diameter is mechanically steered to access different locations on the cornea sequentially. The scanning beam method usually can be used to achieve a desired shaping profile with a better accuracy than that of the uniform beam method.
In many prior-art PRK procedures, a corrective operation is usually done in four steps. First, a desired topographic shape of the cornea of an eye is determined based on the specific vision problems in the eye. Secondly, the operating parameters, such as the total desired ablation depth and thereby the required number of pulses, are determined prior to the operation for the desired cornea shape. For a scanning PRK, a desired trace of the scanning beam also needs to be determined. Thirdly, the predetermined parameters are used to control the laser to perform the corrective procedure by reshaping the cornea. Lastly, the resultant topographical shape of the cornea is measured.
The above prior-art approach requires that all predetermined operating parameters remain constant during operation. For example, the laser fluence must be precisely known and remain constant during the entire operation. The topographic measurement is performed after the operation and only then can the success of the operation be evaluated.
However, a number of practical factors may adversely affect the above approach. For example, the corneal tissue may not be even and the absorption coefficient of a cornea can often have local variations. This may cause variations in the ablation depth at different locations on the cornea for a laser beam of a constant fluence. Thus, the final topographic shape of the cornea may deviate from a desired shape and the resultant vision can be significantly degraded.
The output power of a laser may also vary or fluctuate during an operation. This power drift in the laser beam can be caused by many factors, including temperature variations, mechanical vibrations, noise in the laser electronic control circuits and so on. In many cases, these factors are not easily controllable although various control servo techniques may be used to reduce the variations. The power variation of the laser can cause undesirable variations in the laser fluence. Consequently, the ablation depth of a pulse changes.
Furthermore, the alignment of the beam scanning system is known to change as well due to variations in the relative positioning of the laser and the beam scanning system, variations in the beam scanning system, and beam drift of the laser. This can cause the scanning laser beam to walk off from a prespecified scanning trace in a scanning PRK process, thereby resulting in an error in the final shape of the cornea. Any accidental movement of the eye during the operation could also adversely affect the operation.
Errors in the final corneal shape due to the above and other factors significantly reduce the effectiveness of the PRK procedures. A study of patients who were treated with a conventional PRK at the Doheny Eye Institute of the University of Southern California showed that about 95% of the patients achieved a corrected vision acuity 20/40 or better after the surgery (corresponding to a refractive error of less than 1 diopter) and only about 50% of these patients had a corrected vision acuity of 20/20 or better. The current relatively low success probability of PRK at least in part contributes to the existing doubt of the public on the PRK procedures despite many benefits and advantages of the PRK over the use of the corrective eye glasses or invasive surgical procedures. Many practitioners in the ophthalmology community believe that a success probability above 95% in achieving a corrected visual acuity of 20/20 with PRK may be necessary in convincing more people with visual problems to receive the beneficial PRK treatment.
In recognition of the above, it is desirable to have precise active control of the ablation progress in real time in order to compensate for the above variations during a PRK operation. This requires acquisition of corneal topographic data of the 3-dimensional shape of the corneal surface within the time interval between two successive ablating pulses. In this context, the topographic measurements are performed in "real time". The topographic data is then fed back to the diaphragm/beam-steering control system to adjust the operating parameters. This active feedback control mechanism can be used to minimize the deviation of the final corneal shape from the ideal shape during the operation.
In order to ascertain the results of the operation, resolution of 0.1 diopters in the corneal curvature measurement would be desirable. The amount of diopter correction as function of ablation depth at the center of the cornea can be calculated geometrically.
The result for the case of myopia is shown in FIG. 1. The curve in FIG. 1 shows that 0.1 diopters correspond to an ablation depth of about 1.3 .mu.m which can be achieved with roughly 4-7 laser pulses in a typical PRK system. At a pulse repetition rate of 50 Hz, this requires one complete topographical measurement every 80 msec or faster. In a transverse direction along a corneal surface, the resolution is mainly determined by the pixel size of the camera and the apertures of the optics used in the optical system. A typical camera can provide a resolution of about 250,000 pixels. If the entire corneal surface, typically about 29 mm.sup.2 in area, is imaged on the camera, an effective spatial resolution of approximately 10 .mu.m is obtained. Commercial systems typically have a resolution on the order of a few hundred microns. Assuming an acceptable lateral resolution at 100 .mu.m in the beam diameter spot, about 2,500 of pixels need to be processed.
The measured topographic data can be used both for graphical display and feedback to the beam-steering controls of the system. To account for delays in the calculation of the required mirror positions and the mechanical response, a faster operation of the measurement system may be reasonably assumed. One estimate for the data processing rate is 30 ms or 30 Hz, which corresponds to the standard video rate. This leads to approximately 83,000 pixels per second.
However, the conventional corneal topographic systems are limited in providing the above real-time topographic measurements during the surgery. One commercial corneal topography system, for example, projects calibrated fringe patterns on the cornea, captures the reflection using a CCD camera, and then digitally processes the distortions on the fringe pattern in order to deduce the deviation of corneal surface from a perfect sphere. The amount of calculation required to perform this operation cannot be performed at a speed of 83,000 pixels/sec that is desirable for a real-time.
In addition, the conventional corneal topographic systems impose various other constraints that make them unsuitable for real-time surgical monitoring.
For example, several commercial topographic systems project Placido rings on a corneal surface and capture the specular reflected pattern from the cornea with a camera. The captured pattern is then digitized and measured to determine the fringe distortion. Thus, an one-to-one mapping between the surface deformation and the fringe shape is established. One limitation of this approach is the long processing time, usually on the order of 10 seconds or 0.1 Hz in terms of the processing rate. This is too slow for a real-time corneal topographic measurement required for a PRK treatment. Another limitation is that the Placido ring technique may work well on smooth specularly reflective surfaces but the performance is severely degraded for a scattering or diffusive surface. In a PRK surgery, the epithelium on a corneal surface is removed so that the surface is no longer perfectly specular but has a degree of scattering due to the laser ablation. This can undermine the effectiveness of the Placido ring method in a real-time corneal topography during a PRK operation. In addition, the Placido ring method requires the imaging camera to be placed at certain right angles to capture the fringes. This may limit the access of the ablating laser beam to the cornea.
A triangulation technique is also used as a conventional topographic method. A computer controls the pitch of the projected fringes on the corneal surface and acquires the images from the camera. The captured images are processed to obtain the fringe edge distortion data which constructs an isoheight map of the corneal surface. In a binocular configuration, the position of a point of interest on a corneal surface is extracted in three-dimensional space by intersecting the lines connecting the point to two cameras.
One limitation in the binocular-triangulation-based technique is the need to have a reference point on the cornea for a 3D mapping. This is difficult to obtain for a corneal surface which lacks pronounced features (e.g. a shape with edges and texture). Another limitation is the requirement to obtain a nearly perfect calibration, since a slight error in the knowledge about the relative location of the two cameras can induce large errors in the inferred surface shape.
Alternatively, a monocular configuration may be used for a triangulation system. Only a single camera is needed. A light projector can effectively serve as a second, active camera to replace a second passive camera in the above binocular configuration. A reference point is no longer necessary in the monocular technique. The light projector is used to project fringe or grid patterns of varying spatial frequency on the cornea. The topographic information is obtained by observing the deformations in the fringe edges.
Commercial corneal topographers based on triangulation can be used for a scattering corneal surface and allow access to a corneal surface by a ablating laser beam. Since the camera images a scattering surface at an angle, only a small portion of the reflected light from the surface may be captured. Therefore, it is often necessary to deposit a reflectivity enhancing material such as sodium fluorescein on the cornea in order to improve its reflectivity. The processing speed is usually slow, typically on an order of 5 to 10 seconds for a full corneal shape on which about 1000 points are sampled. In addition, the imaging resolution is about 0.2 mm.
Coherent holographic interference has also been used in some commercial topographers. Some aspects of this approach can be found, for example, in Am. J. Optometry & Phys. Optics, Vol. 65(8), pp. 653-660 (1988) by Smolek and in J. Cataract Refract. Surg., Vol.19S, pp. 182-187 (1993) by Burris et al. One limitation of this technique is the inherent speckle noise in a coherent holographic system. The inventors of the present invention evaluated this method for corneal shape measurements on swine eyes by both calculations and experiments. It was found that strong speckle noise was present in the captured images by illuminating the surface of a swine eye without the epithelium with a laser beam. The speckle noise makes it very difficult to form a topographic measurement. Well-known speckle reduction techniques, such as those disclosed by Iwai and Asakura in "Speckle reduction in coherent information processing", IEEE proceedings, Vol. 84(5), pp. 765-781 (1996), are usually cumbersome to incorporate in a commercial system, and cannot completely eliminate the speckle noise since they are incompatible with holographic recording.
The holographic techniques also suffer from power and stability limitations. The allowable power that may be applied on an eye without causing damage is within a range approximately from about 300 .mu.W to about 400 .mu.W. A reflected light beam with about 6-8 .mu.W is usually available for recording a hologram for a typical eye with a reflectivity of about 2%. Conventional photopolymers are reasonably sensitive media in the red region of the spectrum. The time required to accumulate enough energy to record a hologram in such material would be on the order of a few hundred milliseconds, during which the patient's eye and the optical system must be completely stabilized. This is difficult in practice because of periodic eye movements and other instabilities that may occur under surgery room conditions.